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Estimation of the lifetime distribution of the parts from the autopsy statistics of the machine

Published online by Cambridge University Press:  14 July 2016

Isaac Meilijson
Isaac Meilijson*
Affiliation:
Tel-Aviv University
*
∗Postal address: Department of Statistics, Faculty of Social Sciences, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel.
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Abstract

Given a coherent reliability system, let Z be the age of the machine at breakdown, and I the set of parts dead by time Z. We prove that if all lifetime distributions are non-atomic and share the same essential extrema, and if the incidence matrix of the minimal cut sets has rank equal to the number of parts, then the joint distribution of Z and I determines uniquely the lifetime distribution of each part. We present a Newton–Kantorovič iterative method for the computation of those distributions. We deal informally with the relaxation of the assumptions and with the statistical problem where instead of the joint distribution of Z and I we have an empirical estimate of this joint distribution.

Keywords

COMPETING RISKSCOHERENT RELIABILITY SYSTEMSLIFETIME DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 4 , December 1981 , pp. 829 - 838
Copyright
Copyright © Applied Probability Trust 1981 

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Footnotes

This work was concluded during the author's visit to the Vrije Universiteit, Amsterdam.

References

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